B- If x+ 2 cos0 prove that x" +2 cosro by used complex number.

Q: Express as a product:cos 3θ - cos 8θ

A: Known fact: cosC-cosD=2sinC+D2 sinC-D2.

Q: (b) Show that i³i is real, even though i or 3i is not.

A:

Q: 5. Solve 2tan?x +3tanx – 2 = 0 exactly over the set of real numbers in radians.

A:

Q: show that cos 6x = cos 2x (4cos2 2x-3)

A: Given,           To prove: cos 6x = cos 2x (4cos2 2x-3)

Q: using De-Moivre's theorem prove that cos π/7, cos 3π/7 and cos 5π/7 are the roots of 8x3-4x2-4x+1=0.…

A: The given equation 8x3-4x2-4x+1=0 Roots of the equation are cosπ7, cos3π7, cos5π7 use trigonometric…

Q: is: The number of zeros of sin(-) is: `z-1

A: If y=f(z), then the variable z is called the input of the function, and y is called the output of…

Q: (b) Show that i0 is real, even though i or 6i is not.

A:

Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: Solve for x: 6 Cos +7Sin x -8

A:

Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de =- (1-cos a). CO TE/2-a

A: We will use the Differentiation under Integral sign method, to solve the problem.

Q: Express in terms of i. --4 %3! --4 (Simplify your answer. Type your answer in the form a + bi.)

A: We find the solution by finding the sq. root of the number.

Q: Find the product of z1 = 2 (cos 213° + i sin 213 °) and Z2 = 4 (cos 33 ° + i sin 33 °) %3D

A:

Q: Find the last (right) two digits of 77'. use Euler's theorem to solve it

A: We need to find the last two digits of 777. To find the last 2 digits means we need to find the…

Q: 2. Express cos(60) in terms of powers of cos only.

A:

Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

Q: Prove that (7 sin2m-10 cos2n-10 = – B(m,n)

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Express in a + bi form. 7+i 3 2i

A:

Q: Determine whether the positive or negative square root should be selected. 1+ cos 565° cos 282.5° =…

A:

Q: 10. Prove that (지12 sin 8 cos 1 (cos a cosec 0) de 1/2-a (1-cos a )

A:

Q: 10. Prove that 7/2 sin 0 cos (cos a cosec 0) do -(1-cos a). 2 ||

A:

Q: What are all of the solutions for the equation 2sin²(θ) + 3sin(θ) + 1 = 0 on the interval of [0,…

A: solution:-2sin²(θ) + 3sin(θ) + 1 = 0,    θ∈ [0, 2π)2sin²(θ) + 2sin(θ)+sin(θ) + 1 =…

Q: Find sin 8. 4/5 4|5 m15

A: Take point in parametric form and compare with given point then solve

Q: Express 9[cos(60°) - isin(60°)] in the form a + bi

A:

Q: Find the last (right) two digits of 77". use Euler's theorem to solve it

A: we have to find the last two digits of 777

Q: (b) Show that it is real, even though i or 8i is not.

A:

Q: Express as a product:3 cos 2x + 3 cos 6x

A: 3cos2x+3cos6x we have to express as product

Q: Express in terms of i -294 -294 = (Simplify youlanswer. Type your answer in the form a + bi.)

A:

Q: B- If x+! += 2 cos prove that x"+= 2 cos rø by used complex number.

A: we have to show that the following

Q: prove that: a- cos20 = cos²0 – sin²0 %3D sin20 = 2sin0cos

A:

Q: Express in terms of i <-294 %3D (Simplify youlanswer. Type your answer in the form a+ bi.)

A: √(-294)=7√(6)i

Q: Prove that cos 17° + sin17° tan62° %3D cos17° – sin17°

A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: 4. Prove that equations are identities. l– cos4x a) tan 2x =, 1+ cos 4x

A: Given:

Q: Let z=x+iy be a complex number such that coshz#0. Then Im(tanhz) is equal to

A: None of these is correct.

Q: prove it 5. 2 sin (3x) = 1– cos(6x)

A:

Q: Give the general soulution for 5cos2x-1=-cos2x+2

A:

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A: Given, 22+i2212  We have to write the answer in the form of a+ib using De Moivre's theorem.

Q: Prove that 3 12 56 -1 -+ cos 5 sin sin 13 65

A:

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A:

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A: Given expression is (23+2i)-5 We have to use De Moiver's theorem to simplified the answer in the…

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A:

Q: Use the addition formula to prove                                                             cos 3θ…

A:

Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: do o find 4+ 3 sin 0

A:

Q: 5, in sinh (3,412 – 13,4) aluate the following complex expressions. Box ur final

A:

Q: Prove cos 4x = 8 cos4 x - 8 cos2 x +1.

A: In trigonometric ratio,cos2θ=2cos2θ-1

Q: Determine 1-/[e-tt sin(2t)] 2- 23+3s)*

A: Given

Q: 17 prove 4 Cos" ☺ - Sin" 0 = Cos20

A:

Q: show that. 19 -18 O Sin 8= ē-e 2) Sin(-9) = -Sing 3) coshio = cose %3D 2.

A: Here we use the properties of trigonometric functions and hyperbolic function.

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A:

Q: Find the exact value of:

A: Given that, To find the exact value of  sin 7π12 by using the identity, sin ( A + B) = sin A cos B…